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JEE Main 2021 (Online) 18th March Evening Shift
Numerical  +4  -1
The projectile motion of a particle of mass 5 g is shown in the figure.

The initial velocity of the particle is $$5\sqrt 2$$ ms-1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is x $$\times$$ 10-2 kgms-1. The value of x, to the nearest integer, is __________.
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JEE Main 2021 (Online) 18th March Morning Shift
Numerical  +4  -1
A ball of mass 10 kg moving with a velocity 10$$\sqrt 3$$ m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30$$^\circ$$ with respect to the x-axis. The velocity of the ball moving at 30$$^\circ$$ with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is ____________.

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JEE Main 2021 (Online) 17th March Evening Shift
Numerical  +4  -1
The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $${x \over 3}{a \over \pi },{x \over 3}{a \over \pi }$$ where x is _____________. (Round off to the Nearest Integer).

[a is an area as shown in the figure]

A force $$\overrightarrow F$$ = $${4\widehat i + 3t\widehat j + 4\widehat k}$$ is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ___________. (Round off to the Nearest Integer)